Contemporarily, cotton fiber cleaning machines work as a rule in a pneumatic/mechanical manner by guiding the tufts in an air stream around a cylinder (cleaning and opening cylinder) which rotates around its axis and is equipped with mechanical cleaning elements. Simultaneously, the tufts are moved past stationary mechanical cleaning elements. The cotton fibers are supplied with pneumatic means,-are brought to the cleaning elements and are transported away from them again. In the course of these events, the cotton fibers are cleaned with mechanical means. This interrelation of pneumatic and mechanical means can be controlled under certain conditions in the operation of the transporting pneumatic means. However, this has the disadvantage of mixing the transport function with the cleaning function, i.e. the jet of air with uncleaned fibers comes from one section in which the transporting function predominates into a section in which the cleaning function predominates and the transport function vanishes in a common process function until, in a subsequent section, it returns into the transport function.